Question

Let ​ x2−20x=10 .​

What values make an equivalent number sentence after completing the square?

Enter your answers in the boxes.

​ x2−20x+______=______ (whats the answer for the 2 underlines?)

Answer 1

The given expression is
`x^(2) -20x =10`

This is of the form
`ax^(2) +bx=c`

Comparing the equations a=1,b=-20 and c=10.

To complete the square we take half then coefficient of x that is b and square it .This is added to both sides of the equation.

The coefficient of x is 20 .Half of it is 10 .Square of 10 is 100.

`(b)/(2a) =(-20)/(2)= -10`

`(-10)^(2) =100`

This 100 is added to both sides.The equation becomes:
`x^(2) -20x +100=20+100`

Or
`x^(2) -20x+100 =110`

Answer 2

- 20 / 2 = - 10

(- 10)² = 100

x² - 20x + 100 = 10 + 100

x² - 20x + 100 = 110